Stability of hydraulic fall and sub-critical cnoidal waves in water flows over a bump

A forced Korteweg–de Vries (fKdV) equation can be used to model the surface wave of a two-dimensional water flow over a bump when the upstream Froude number is near one. The fKdV model typically has four types of solutions: sub-critical cnoidal waves, sub-critical hydraulic fall, transcritical upstream soliton radiation, and supercritical multiple solitary waves. This paper provides a numerical demonstration of the stability of the hydraulic falls and cnoidal waves solutions.     

On pseudo-uniform flow in open channel hydraulics

Summary The differential equation that governs the longitudinal variation of the surface profileh(x) in steady plane channel flow is qualitatively discussed for the case of pseudo-uniform flow states. The solutions are either of the cnoidal or solitary wave type. It is shown that, among all cnoidal waves, solitary waves have minimum energy head. Further, surface profiles mustbreak whenever the Froude-number exceeds the value (which is close to experimentally determined values). The model equations are applied to the undular hydraulic jump, and it is shown how the equations can be used in practical situations of open channel flow hydraulics.With 11 Figures     

On the limit of subcritical free-surface flow over an obstruction

Summary In this note, through studying an asymptotically reduced equation which is a forced Korteweg-de Vries equation, an analytical expression of Forbes' hydraulic fall solution is obtained. It is pointed out that Forbes' solution of a hydraulic fall over an obstruction is the limit of cnoidal wave solutions as the upstream Froude number approaches a certain value less than one from below.     

A model equation for steady surface waves over a bump

The objective of this paper is to study the solutions of a model equation for steady surface waves on an ideal fluid over a semicircular or semielliptical bump. For upstream Froude number F>1, we show that the numerical solution of the equation has two branches and there is a cut-off value of F below which no solution exists. For F<1, the problem is reformulated to overcome the so-called infinite-mass dilemma. A branch of solutions and a cut-off value of F, above which no solution exists, are found. Furthermore, we also obtain a branch of hydraulic-fall solutions which decrease monotonically from upstream to downstream.     

Effects of an airfoil and shock waves on vortex shedding process behind a square cylinder

Summary Effects of an airfoil and shock waves on vortex shedding process behind a square cylinder have been examined experimentally at a Mach number of about 0.91 and at a Reynolds number (based on the side lengthD of the square cylinder) of about 4.2×10⁵. The main experimental parameter is the spacing ratioL/D, and is varied from 1.125 to 5.5, whereL is the spacing between the square cylinder and the airfoil.It is found that similarly to the case at subcritical Mach numbers at the supercritical Mach number there exist three patterns of the flow around the square cylinder and airfoil arranged in tandem depending upon the spacing ratioL/D: In the first flow pattern with small spacing ratio, the downstream airfoil is enclosed completely in the vortex formation region of the square cylinder. In the second flow pattern, the shear layers separating from the square cylinder reattach to the airfoil. In the third flow pattern with large spacing the shear layers roll up upstream of the airfoil. The Strouhal number at the supercritical Mach number is higher than that at the subcritical Mach numbers. Shock waves hasten the vortex shedding behind the square cylinder by decreasing the area of asymmetrical part of the vortex formation region with respect to the wake axis, and let the streamwise length of the separating shear layers longer than otherwise.With 8 Figures     

A note on waveless subcritical flow past a submerged semi-ellipse

The flow of water over a broad obstruction usually creates a downstream wave train. However, it has been shown that for some objects and discrete values of flow rate and height and length of the obstruction, there are no downstream waves – and hence zero wave drag on the object. Here we revisit this problem and complete an examination of the parameter space for flow over a semi-ellipse. A rich pattern of waveless solutions that merge into each other is detected.     

Longitudinal and transverse waves in anisotropic elastic materials

Summary It is shown that a necessary and sufficient condition for a longitudinal wave to propagate in the direction n in an anisotropic elastic material is that the elastic stiffness C ₁₁ (n) is a stationary value (maximum, minimum or saddle point) at n. Explicit expressions of all n and the corresponding elastic stiffness C ₁₁ (n) for which a longitudinal wave can propagate are presented for orthotropic, tetragonal, trigonal, hexagonal and cubic materials. As to longitudinal waves in triclinic and monoclinic materials, only few explicit expressions are possible. We also present necessary and sufficient conditions for a transverse wave to propagate in the direction n. As an illustration, explicit expressions of all n, the polarization vector a and the wave speed c for which a transverse wave can propagate in cubic and hexagonal materials are given. The search for n in hexagonal materials confirms the known fact that a transverse wave can propagate in any direction. A longitudinal wave is necessarily accompanied by two transverse waves. However, a transverse wave can propagate without being accompanied by a longitudinal wave.     

Free-surface flow over a polygonal and smooth topography

Summary The study of two-dimensional, irrotational, inviscid, incompressible steady state motion generated by a polygonal and a smooth obstruction, is made in terms of the linearized theory. The bottom is represented in integral form using Fourier's double integral theorem. Then following Lamb [1], a linear free-surface profile is obtained for the supercritical and subcritical cases. The results are plotted and discussed for the two cases of the flow for different shapes of the bottom and different values of Froude number,F.     

A probabilistic approach for thermal shock fatigue life of glass

This paper presents a probabilistic approach for predicting fatigue life of glass subjected to near‐ΔT_C (critical temperature difference) thermal shock which exhibits little subcritical crack extension. First, thermal shock fatigue life N_f was derived as a function of temperature difference ΔT, fracture probability F and Biot's modulus β from the slow crack growth concept in conjunction with the Weibull distribution model. Next, thermal shock fatigue tests as well as flexural tests were performed for borosilicate glass to measure ΔT_C and N_f versus ΔT. The parameters associated with slow crack growth were then determined from the experimental results while the heat transfer coefficient h or β was obtained with the aid of finite element analysis. Thirdly, the thermal shock fatigue diagram (ΔT?N_f curves) was depicted for various values of β. Finally, crack length was simulated on the basis of the present approach.     

Comparison of fluorocarbon film deposition by pulsed/continuous wave and downstream radio frequency plasmas

Fluorocarbon (FC) films have been deposited using pulsed and continuous wave (cw) radio frequency (rf) plasmas fed with hexafluoroethane (C₂F₆), octafluoropropane (C₃F₈), or octafluorocyclobutane (C₄F₈). The effects of feed gases used, discharge pressure, rf power, substrate positions and discharge modes (pulsed or cw) on the deposited films are examined. Film properties are determined using X-ray photoelectron spectroscopy, atomic force microscopy, and static contact angle measurements. The contact angles of FC films are well related to their compositions and structures. Feed gases used, discharge pressure, rf power, substrate positions and discharge modes strongly affect the morphology of the resulting film, as revealed by atomic force microscopy. Optical emission spectrometry measurements were performed to in-situ characterize the gas-phase compositions of the plasmas and radicals’ emission intensities during film deposition. Correlations between film properties, gas-phase plasma diagnostic data, and film growth processes were discussed. The film growth in pulsed or downstream plasmas was controlled by the surface migration of radicals, such as CF₂ towards nucleation centers, which result in the deposition of FC films with less cross-linked nature and rougher surfaces. These results demonstrate that it is possible to control film compositions and surface structure by changing deposition parameters.     

Properties of high-T C Copper Oxides from Band Models of Spin–Phonon Coupling

The mechanism of spin–phonon coupling (SPC) and possible consequences for the properties of high-T _C copper oxides are presented. The results are based on ab initio LMTO band calculations and a nearly free-electron (NFE) model of the band near E _F . Many observed properties are compatible with SPC, as for the relation between doping and for spin excitations and their energy dependence. The main pseudogap is caused by SPC and waves along [1,0,0], but it is suggested that secondary waves, generated along [1,1,0], contribute to a ‘waterfall’ structure. Conditions for optimal T _C , and the possibilities for spin enhancement at the surface are discussed.      

Core electron level structure in C<Subscript>60</Subscript>F<Subscript>18</Subscript> and C<Subscript>60</Subscript>F<Subscript>36</Subscript> fluorinated fullerenes

The structure of C1s and F1s core electron levels in C₆₀F₁₈ and C₆₀F₃₆ fluorinated fullerenes has been studied by X-ray photoelectron spectroscopy using synchrotron radiation. It is established that C1s levels of carbon atoms not bound to fluorine in these compounds are shifted down by 1.0 and 1.6 eV relative to the C1s level in the usual C₆₀ fullerene, so that the binding energies of the core electron levels in C₆₀F₁₈ and C₆₀F₃₆ amount to E _b (C1s, C-C) = 285.7 and 286.3 eV, respectively. These values are characteristic and can be used for the identification of both homogeneous fluorinated fullerenes and combined materials comprising a mixture of various fluorinated fullerenes with each other and with different carbon-containing based materials.     

Single Crystal of C60F X and the X-Ray Structural Analysis

Abstract

Single crystals of fluorinated fullerene C₆₀F _x have been grown by sublimation. The crystal, ca. C₆₀F₄₆, has an fcc lattice with the cell constant 17.158(3) Å. The rotating molecules can be regarded as two inner spherical shells of carbon with radii 3.13 and 3.83 Å and an outer spherical shell of fluorine at 5.12 Å away from the center. PM3 calculations on C₆₀F_44,46,48 support the electron distribution in the ca. C₆₀F₄₆ determined by the X-ray structural analysis.     

On longitudinal and transverse variations of the bed shear stress on the wetted perimeter of a sloped rectangular open channel in a hydraulic jump

Summary This paper is concerned with longitudinal and transverse variations of the sear stress on the wetted perimeter of a sloped rectangular open channel in a hydraulic jump. It is found that the locus of the maximum bed shear stress upstream and downstream of the hydraulic jump indicates a clear meandering tendency. That is, the meandering locus of the maximum bed shear stress appears whether the flow is supercritical or subcritical. In the jump region, the locus almost follows the central axis of the channel, and the amplitude and wave-length are very small. However, downstream of the jump region the locus of the maximum bed shear stress starts meandering, and the amplitude and wave-length vary in an irregular manner.     

A Study of the Flow through Capillary Tubes Tuned for a Cooling Circuit with Saturated Fluorocarbon Refrigerants

Capillary tube expansion devices are widely used in refrigeration equipment; nevertheless, the mechanism of the flow is still not fully described and understood, so the experimental verification of most predictions is still necessary. A modified numerical model of capillary flow has been developed both for standard refrigerants and with emphasis for saturated fluorocarbon (C₂F_2n+2) refrigerants. These refrigerants have several unique properties (high dielectric performance, chemical stability, and radiation resistance). Therefore, they can be used in some special applications, where other common fluids cannot be applied. The main aim of this study was to prepare a practical capillary flow model, which would improve the procedure of predicting the behavior of capillary tubes for cooling circuits of particle detectors being built at the international CERN laboratory in Geneva. The generated numerical model was verified through available data from the literature and also via measurements performed in a real cooling circuit with pure, oil-free octafluoropropane (C₃F₈) refrigerant. Paper presented at the Seventeenth European Conference on Thermophysical Properties, September 5–8, 2005, Bratislava, Slovak Republic.     

p, @rho, T, x-Relations for Water–Hydrocarbon Gaseous Mixtures in a Wide Range of the Parameters of State

Experimental data on p, @rho, T, x-Relations (gas phase) of the water–hydrocarbon binary systems (CH₄–C₈H₁₈, C₆H₆, C₇H₈) are given in the subcritical and supercritical regions, including states close to the critical region, at temperatures from 523.15 to 673.15 K and pressures up to 63 MPa, obtained by the piezometer method at constant volume. The special features of the thermodynamic behavior of mixtures of this class are determined.     

MOLECULAR AND CRYSTAL STRUCTURE OF THE ADDUCTS OF C60F18 WITH AROMATIC HYDROCARBONS

ABSTRACT

The solubility of C₆₀F₁₈ in aromatic hydrocarbons, benzene, toluene, and xylenes (0.48–1.23?mg/mL), and decomposition enthalpies for the 1?:?1 and 1?:?2 complexes (31–70?kJ/mole) have been determined. The C₆₀F₁₈ molecule has near perfect C_3v symmetry, and the x-ray single-crystal structures of the C₆₀F₁₈?L complexes (L=hexamethylbenzene, o-, m-, p-xylene, and bromobenzene) are compared in terms of 12 types of C?C and four types of C–F bonds. Analysis of the packing modes in the crystals shows an influence of the size and polarity of the aromatic hydrocarbon molecule.     

Time-domain dielectric relaxation in polyamide 6, poly(vinyl chloride), ethylene-vinyl acetate copolymer and poly(vinylidene fluoride)

The time-domain dielectric responses of polyamide 6 (PA6), poly(vinyl chloride) (PVC), ethylene-vinyl acetate copolymer (EVA) and poly(vinylidene fluoride) (PVDF) to a voltage step were measured at different temperatures. From the variation of the sample capacitance,C, with time, the ratioF _d/C was determined, whereF _d = (dC/dlnt)_max is the maximum (inflexion) slope of the capacitance versus log(time) dipole response curve, and C is the difference between the initial and the extrapolated equilibrium capacitance values. A modified KohIrausch-WiIIiams-Watts (stretched exponential) function provided a good fit to the measuredC(t) data. For low temperatures, typically below – 20°C,F _d/C, is about 0.1, characteristic of highly cooperative relaxation, while at higher temperatures the ratio approaches 1/e, characteristic of nearly independent (Maxwellian) relaxation. This is in contrast to corresponding analyses of mechanical relaxation in solids for which the constant is almost always near 0.1 at room temperature.     

Withdrawal from a fluid of finite depth through a line sink, including surface-tension effects

The steady withdrawal of an inviscid fluid of finite depth into a line sink is considered for the case in which surface tension is acting on the free surface. The problem is solved numerically by use of a boundary-integral-equation method. It is shown that the flow depends on the Froude number, F _B=m(gH ³ _B)^–1/2, and the nondimensional sink depth =H _S/H _B, where m is the sink strength, g the acceleration of gravity, H _B is the total depth upstream, H _S is the height of the sink, and on the surface tension, T. Solutions are obtained in which the free surface has a stagnation point above the sink, and it is found that these exist for almost all Froude numbers less than unity. A train of steady waves is found on the free surface for very small values of the surface tension, while for larger values of surface tension the waves disappear, leaving a waveless free surface. It the sink is a long way off the bottom, the solutions break down at a Froude number which appears to be bounded by a region containing solutions with a cusp in the surface. For certain values of the parameters, two solutions can be obtained.     

Addition of the Lewis Acid Zn(C6F5)2 Enables Organic Transistors with a Maximum Hole Mobility in Excess of 20 cm2 V−1 s−1

Incorporating the molecular organic Lewis acid tris(pentafluorophenyl)borane [B(C₆F₅)₃] into organic semiconductors has shown remarkable promise in recent years for controlling the operating characteristics and performance of various opto/electronic devices, including, light‐emitting diodes, solar cells, and organic thin‐film transistors (OTFTs). Despite the demonstrated potential, however, to date most of the work has been limited to B(C₆F₅)₃ with the latter serving as the prototypical air‐stable molecular Lewis acid system. Herein, the use of bis(pentafluorophenyl)zinc [Zn(C₆F₅)₂] is reported as an alternative Lewis acid additive in high‐hole‐mobility OTFTs based on small‐molecule:polymer blends comprising 2,7‐dioctyl[1]benzothieno [3,2‐b][1]benzothiophene and indacenodithiophene–benzothiadiazole. Systematic analysis of the materials and device characteristics supports the hypothesis that Zn(C₆F₅)₂ acts simultaneously as a p‐dopant and a microstructure modifier. It is proposed that it is the combination of these synergistic effects that leads to OTFTs with a maximum hole mobility value of 21.5 cm² V^?1 s^?1. The work not only highlights Zn(C₆F₅)₂ as a promising new additive for next‐generation optoelectronic devices, but also opens up new avenues in the search for high‐mobility organic semiconductors.